This one is slightly tricky..

in the first sentence, after "through actions such as" several actions are listed.
"improving the morale of a demoralized nation" is clearly not one of those actions. Rather this phrase runs parallel to " By confronting a devastated economy"

the correct way to put it would be

" By confronting a devastated economy through actions such as (a),(b),(c) and (d) and by improving the morale of demoralized nation through his (e),(f) and (g),"


A)launching massive public works programs, and improving the morale of a demoralized nation through his fireside chats ( this is wrong because here 'improving the morale' phrase is included as one of the actions that confronted the economy)
B)and launching massive public works programs, and improving the morale of a demoralized nation through his fireside chats ( wrong parallelism , should be "by confronting a devastated .... and by improving the morale)
C)and launching massive public works programs, and by improving the morale of a nation demoralized through his fireside chats ( this seems to suggest that the nation was demoralized by his speeches)
D)and through the launch of massive public works programs, and by improving the morale of a demoralized nation through his fireside chats ( " launching massive PW programs" is one of the actions through which the economy was confronted, it is mentioned as a separate action here )
E)and launching massive public works programs, and by improving the morale of a demoralized nation through his fireside chats - this is the sentence the correctly sounds like the one i mentioned above.

This question is primarily testing Parallelism. It's a bit confusing because the Parallelism is working on two levels:

"By CONFRONTING...and By IMPROVING..."

and then also the items that are listed as the actions Roosevelt took to confront the economy:

"...such as CREATING..., OPENING..., SUSPENDING...,LAUNCHING...,"

Since the Fireside chats and speeches don't logically have anything to do with the economy, they shouldn't be part of the items listed as actions taken to help "confront a devastated economy."

I like this question since it highlights the importance of Meaning in SC as well. Technically (A) is parallel, but the meaning isn't quite right! A good reminder to all of us not to simply be grammar robots.

By confronting || By improving

Confronting has got some action such as creating, opening, suspending and launching
Improving has got another set of actions

Using the above logic's, E is the best answer.